I am working on a building where the previous owner had been in the process of adding a second story floor to a 500 sq. ft add-on room. He secured the floor joists into holes cut into the cinder block wall on the east side of the room, but abandoned the project and left the other end of the joists resting on jacks on the west side.

Now, I am left with the task of securing the joists to the BRICK wall on the west side and finishing the floor. The room was an add-on to a brick building and the previous owner used cinder block, so half the room is brick, the other half cinder.

THE QUESTION: I need some advice on how to secure the floor joists to the double brick wall on the west side of the room. I was considering bolting a long strip of angle iron to the brick and resting the joists on that.

You should be contacting an engineer. I know this is a DIY site, however, this part is not DIY.
You live in tornado alley, something which needs to be considered as this will effect the building.
Your on the right track with through bolts and ledgers, just get someone who is there looking at the project and spend your $$ wisely.
Also find out what your Building official wants to see in your location.
Certain sized bolts, threaded rod and washer sizes will be answered by the engineer. Probably around $400-500. $$ well spent.